Study finds an efficient algorithm for measuring integrated information in large neural systems.
problem Finding the Minimum Information Partition (MIP) for measuring integrated information in large neural systems is computationally expensive.
method Developed an optimization algorithm that can find the MIP in polynomial time for non-submodular measures of integrated information.
result The algorithm accurately identifies the MIP in large systems, making it practical for real neural data.
Researchers use orbital integrals to recover group theoretic information from K-theory classes.
problem Recovering group theoretic information from K-theory classes not associated with the discrete series. method Using maps K0(Cr∗G)oC defined by orbital integrals and a fixed point formula for equivariant indices. result Obtained continuity properties and expressions for formal degrees of discrete series representations.
Paper introduces a novel error measure for neural networks integrating statistical and information theory.
problem No single error measure is universally best for neural network training.
method Developed a novel error measure EExpAbs and integrated it into the Levenberg-Marquardt algorithm. result Self-adaptive, dynamic learning algorithm improves both model accuracy and training process.
New method uses iterated integrals to bridge geometric and homotopy information.
problem Lack of effective methods to connect geometric and homotopy information.
method Introducing Chen's iterated integrals on loop spaces.
result Upper bounds for Gromov's distortion and non-existence of small-volume cycles.
We briefly review selected contributions to immersion-theoretic topology, from S. Smale's immersion theory for spheres to M. Gromov's convex integration theory, during the early "golden" period from about 1959-1973. Historical remarks are included and technical concepts are presented informally.
The perturbative Chern-Simons theory for knots in Euclidean space is a linear combination of integrals on configuration spaces. This has been successively studied by Bott and Taubes, Altschuler and Freidel, and Yang. We study it again in terms of degree theory, with a new choice of compactification. This paper is self-…
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
Optimistic algorithms and Thompson sampling use info-theory for better reinforcement learning.
problem Designing algorithms that balance exploration and exploitation in reinforcement learning.
method Integrating information-theoretic concepts into optimistic algorithms and Thompson sampling.
result Cumulative regret bound depends on uncertainty and quantifies prior information value.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
Paper calculates indices for group actions using cocycles.
problem Calculating equivariant indices for group actions.
method Construct cyclic cocycles on Harish-Chandra's Schwartz algebra, compute pairings with equivariant indices.
result Index formula completely determines equivariant indices via topological expressions.
Researchers twist Deligne cohomology for the first time.
problem No new problem introduced; existing Deligne cohomology is already versatile.
method Explicitly twisted Deligne cohomology by taking degree one twists of integral and de Rham cohomology.
result New properties of twisted Deligne cohomology are presented and illustrated.
Mathematical study of learning long-term integration in linear RNNs.
problem How do linear recurrent neural networks learn to integrate over long timescales?
method Analytical study of linear RNNs trained to integrate white noise and damped oscillatory filters.
result Learning dynamics are described by low-dimensional effective equations for outlier eigenvalues.
A theoretical framework for deep learning is proposed to explain its effectiveness.
problem Lack of a comprehensive theory explaining deep learning's effectiveness.
method Integrates three characteristics into a graphical model called neurashed.
result Explains common empirical patterns in deep learning and provides insights into regularization and elasticity.
String geometry theory uniquely determines classical action with T-symmetry.
problem Non-renormalizability and loop corrections in string theory.
method Distinguishes effects of β and ħ parameters, proving no loop corrections.
result No loop corrections in string geometry theory, avoiding non-renormalizability.
CO-BED optimizes experiments using Bayesian methods and information theory.
problem Optimizing experiments in a context-dependent manner.
method Formalizes contextual optimization with Bayesian experimental design, employing information-theoretic principles and black-box variational methods.
result CO-BED provides a general solution for contextual optimization problems.
Study constraints on knot surgery invariants using Seiberg-Witten theory.
problem Understanding invariants of knots in the three-sphere.
method Use Manolescu correction terms and Seiberg-Witten theory.
result Constraints on invariants for knots in the three-sphere.
scICML integrates multi-omics data from single cells using co-clustering.
problem High noise and sparsity in multi-omics data from single cells.
method Information-theoretic co-clustering-based multi-view learning.
result Improves clustering performance and provides biological insights.
A new distance metric derived from information theory and estimation theory.
problem Developing a robust distance metric for complex signal distributions.
method Information-Estimation Metric (IEM) derived from continuous probability density and denoising errors.
result The IEM is a valid global distance metric that adapts to the geometry of complex distributions.
The paper generalizes Yang-Mills theory to study four-manifold topology.
problem Understanding the topology of diffeomorphism groups of four-manifolds.
method Path integral formulation of supersymmetric Yang-Mills coupled to conformal supergravity.
result The invariants may contain nontrivial information about the topology of the diffeomorphism group.
Geometrically interprets integrability of geodesic flow using web theory.
problem Integrability of geodesic flow by quadratic integrals.
method Geometric interpretation through web theory and integrable billiards construction.
result Constructs integrable billiards on surfaces with quadratic geodesic integrals.
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or l…
Suggests stopping criteria for feature selection using mutual information.
problem Automatic determination of optimal feature subset size and stopping criterion.
method Monitoring conditional mutual information (CMI) among groups of variables using Renyi's α-entropy.
result Easy to implement stopping criteria for feature selection.
Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
New method uses information theory to uncover causal relationships in complex systems.
problem Discovering causal relationships in multivariate systems, especially in Bayesian networks and hypergraphs.
method Partial Information Decomposition (PID) to explicitly model higher-order interactions.
result PID components reveal direct causal neighbors and collider relationships in Bayesian networks and multi-tail hyperedges in causal hypergraphs.
Functional integrals explain quantum mechanics and field theory.
problem Explaining quantum mechanics and field theory using functional integrals.
method Describes Feynman's path integral approach to quantum mechanics and field theory.
result Equivalence of path integral formalism to classical mechanics and quantum mechanics.
Hasse principle applied to area-minimizing submanifolds across different homology types.
problem Understanding the behavior of area-minimizing submanifolds in various homology contexts.
method Extending the Hasse principle from number theory to geometric variational problems.
result Recovering information about area-minimizing submanifolds in integral homology from those in real and mod n homology. Detects essential surfaces in knots using character variety intersections.
problem Identifying essential surfaces in knot theory.
method Analyzing intersections in the character variety of hyperbolic knots.
result Intersection points in the character variety detect Seifert surfaces.
Proposes DPGN for integrating physics knowledge into graph networks for climate prediction.
problem Lack of explicit physics knowledge in deep neural networks.
method Integrates implicit physics knowledge from domain experts into latent space of DPGN.
result Significant improvement in climate prediction tasks.
Study compares different integrals for optimal portfolio optimization with insider information.
problem Optimizing portfolios in a financial market with insider information.
method Anticipating stochastic calculus and various integrals (Russo-Vallois forward, Ayed-Kuo, Hitsuda-Skorokhod).
result The Hitsuda-Skorokhod and Ayed-Kuo integrals do not provide a financially meaningful investment strategy.
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It carries information about the Floer homology of large integral surgeries on the knot. Using the exact triangle, we derive inf…
We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaa…
We prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author. In other words, the natural coordinate in a canonical Calabi-Yau family is a canonical coordinate in the sense of Hodge theory. This implies that the higher weight periods direct…
Machine learning identifies key degrees of freedom in physical systems.
problem Identifying important degrees of freedom in complex systems.
method Artificial neural network based on mutual information and RG procedure.
result Extracted Ising critical exponent using machine learning.
A novel framework infers causal direction from symbolic sequences using pattern entropy.
problem Challenges in discovering causal direction from temporal symbolic data.
method Dictionary Based Pattern Entropy (DPE) framework integrating AIT and Shannon Information Theory. result Minimizing pattern level uncertainty yields a robust framework for causal discovery.
The paper develops sum-of-squares relaxations for computing f-divergences.
problem Computing f-divergences from non-centered covariance matrices. method Sum-of-squares relaxations for convex optimization.
result Sum-of-squares relaxations make computations tractable.
Paper connects quantum physics concepts to knot theory.
problem Understanding functional integrals in quantum field theory.
method Conceptualizes Chern-Simons functional integral without measure theory.
result Establishes relationship between Vassiliev invariants and gauge fields.
A new deep learning framework captures multi-scale spatio-temporal dependencies.
problem Designing and analyzing deep learning models for complex spatio-temporal analytics.
method Developed an I2DRNN model with three modules for integrating and learning multi-scale spatio-temporal data. result The I2DRNN model outperforms classical and state-of-the-art models in capturing meaningful multi-scale spatio-temporal dependencies. Unified MTL framework for heterogeneous data integrates shared and task-specific encoders.
problem Efficiently sharing information across multiple tasks with heterogeneous data.
method Dual-encoder framework with task-shared and task-specific encoders.
result Unified algorithm alternates learning task-specific and shared encoders and coefficients.
A new flow on null manifolds yields gradient estimates.
problem Understanding geometric properties of globally null manifolds.
method Introducing a degenerate Ricci-type flow in a Riemannian leaf of the manifold.
result Proved several new gradient estimates for the flow.
New method learns cooperation and competition without direct interaction.
problem Learning cooperation and competition without direct interaction.
method Information-theoretic regularizers to encourage intention revelation or hiding.
result Cooperative policies lead to more reward, competitive to less, in asymmetric games.
We present arguments for the formulation of unified approach to different standard continuous inference methods from partial information. It is claimed that an explicit partition of information into a priori (prior knowledge) and a posteriori information (data) is an important way of standardizing inference approaches …
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
This paper surveys informed machine learning, integrating prior knowledge into ML.
problem Machine learning's limitations with insufficient data.
method Taxonomy and survey of informed machine learning approaches.
result A taxonomy classifies informed machine learning approaches based on knowledge source, representation, and integration.
Proof shows volume equals integral points for certain manifolds.
problem Counting integral points on affine manifolds.
method Rational Ehrhart theory and Fourier analysis.
result Volume equals number of integral points for integral-integral affine manifolds.
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which accommodates the KdV equation and other well known integrable systems. In the case of qua…
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
3-manifolds' volumes match stable integral values.
problem Determining 3-manifold volumes accurately.
method Integral foliated simplicial volume and ergodic theory.
result 3-manifolds' volumes equal stable integral simplicial volumes.